The construction of seating units is fairly standard, normally involving a frame with padding material secured to it in one way or another, over which a pre-sewn cover is slipped and secured. The appearance and firmness of the seat unit require a very close fit of the cover over the padding, resulting in the necessity of very considerable effort in this operation. There is a two-fold adverse effect to this, producing both an unduly large expenditure of time in the installation, and also a tendency toward fatigue and injury to the hands of the operators. It should also be noted that the practice of producing the covers in the first instance results in the completion of the sewing operation with the cover in an inside-out condition. The usual upholstery practice obviously requires a reversing of this by a process similar to turning a sock inside-out. The time involved in this maneuver is obviously significant in any closely-controlled production operation. These problems are particularly acute in the manufacture of vehicle seating, in which the numbers involved in a production run are large enough to attach great significance to the solution of these problems.